2x^2+12x=976

Solution for 2x^2+12x=976 equation:

2x^2+12x=976

We move all terms to the left:

2x^2+12x-(976)=0

a = 2; b = 12; c = -976;
Δ = b2-4ac
Δ = 122-4·2·(-976)
Δ = 7952
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7952}=\sqrt{16*497}=\sqrt{16}*\sqrt{497}=4\sqrt{497}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{497}}{2*2}=\frac{-12-4\sqrt{497}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{497}}{2*2}=\frac{-12+4\sqrt{497}}{4}
$